to the multiple choice question before you have simplified the problem.
For the first set translate: 2x + 1 greater than or equal to 19?
becomes
2x + 1 >= 19
Right off the bat, you can simplify this into a couple of equivalent statements.
1) subtract 1 from each side of the equation
2x >= 18
divide both sides by 2
x >= 9
So now look at the rest of the question. Immediately you can see that the first
statement is true.
We can write x > = 9 as:
x > 9 or x =9
so that shows that the second statement of 9 < x or 9 > x is not correct.
the third statement is a description of a picture. Draw a numberline, and shade
the point at x=9 as a big black dot, then draw a heavy line to the right, This
would be the correct picture.
The fourth statement is reversed and so is false.
Solve the inequality 4x - 6 > 6x - 20
collect like terms. subtract 4x from both sides, and add 20 to both sides
14 > 2 x
divide both sides by 2
7 > x